This is the true danger of the Islamic system. It seems to be an all or nothing proposition. If you embrace Islam you must embrace the idea of the government submitting to the church. This has proven to be disastrous, for the general populations if not the ruling classes, throughout history.
To my way of thinking, with the preponderance of Christian faiths in the US, any attempt to impose the Sharia would result in a general uprising against both Islam and the government. Hell, we damned near have civil war over the display of the Ten Commandments in public buildings, or of Christmas pageants in public schools!